Ring theory

• Can an Artinian Ring Fail to Be Noetherian?
  Artinian commutative rings are Noetherian, but a right Artinian noncommutative ring can fail to be left Noetherian; here is an example.
• How to Make Addition and Multiplication Tables for a Ring or Ideal
  Build ring and ideal operation tables by applying the inherited operations to each pair; see a complete example using Z4 and its ideal {0, 2}.